ECS 210 Summary of Learning

Hi all,

My ECS 210 learning journey has come to an end and I am so excited to share with you my experiences and growth. Kylie Lorenz and I had a lot of fun collaborating together to compile our summary of learning. Thank you, Katia, Mike, Gerry, and especially our seminar leader Joy for being great mentors and sharing your personal experiences in the field of education with us throughout the semester. I look forward to reflecting on the knowledge I gained through this course in my future as an educator. Bye for now,

Miss. S

ECS 210 Social Studies 7 – Mini Unit – Power and Authority in Canada

UNDERSTANDING POWER AND AUTHORITY IN CANADA

Goal: To investigate the processes and structures of power and authority, and the implications for individuals, communities, and nations (Grade 7 Social Studies Curriculum Goal)

Grade Level: Grade 7

Subject: Social Studies

Time Frame: 1 week

Developed by: Miss Giles, Miss MacPherson, Mr. Manson, Mr. Marwick, Miss Schneider

This unit is for Social Studies 7, and explores power and authority within Canada, and specifically within our local Treaty 4 area. We will discuss how different communities govern, the roles of people in positions of power and the ways in which these leaders are “elected.” We will explore both Provincial and Municipal government/leadership, as well as the roles of Elders and Chiefs within Treaty 4. The approach that we will be taking in this lesson is based on a variety of mediums and ways of thinking in order for our students to gain the most information possible. We are approaching teaching the information through a technological format with our Menti, through group work and student-led individualized learning during the research and jigsaw segments, as well as through an overall group discussion of the discovered information.

Unit Plan

We All Have Biases

Literacy is formally defined as the ability to read and write but analyzing curriculum as literacy illuminates many problems with this limited understanding. Firstly, this hidden message behind this definition implies that one can read and write in the dominant language of the society and thus, living in Saskatchewan if you can not read and write in English, you are seen as illiterate. Secondly, the definition fails to address that people can be literate in other subject areas. In lecture, we discussed various examples of being financially, musically, physically, socially, or technology literate which demonstrates the depth to the term literate that is often forgot. Further, we discussed how beyond being able to read literature, everyone has a way of “reading the world” that has been shaped by their personal experiences and unique identities but yet we often fail to acknowledge our personal biases.

Examining the experiences of my upbringing and schooling point to a number of stories that I was implicitly taught which have developed my biases and coloured the lenses I use to “read the world”. Growing up I believed the Canadian Grand narrative that portrays surface elements of what it means to be Canadian such as being passionate about hockey but fails to acknowledge the history of our country. Throughout my schooling, the notion that Canadian history began in 1867 was constantly reiterated showing ignorance to the people who lived on the land prior to European settlement and confederation, and telling the story that “true” Canadians are of European descent. I also grew up believing in the good and bad racism binary and never believed that I was a racist. I developed racist stereotypes through the tv shows that I watched which consisted of dominantly white casts and the city that I was raised in. I moved to Prince Albert at the age of seven from a small white farming community where I had only ever interacted with people who had white skin. I was immediately taught that some areas of Prince Albert were considered safe while others were not and reflecting on this idea shows that the “safe” areas of this city were dominantly populated by white people while the “unsafe” areas were occupied by First Nations. As a young child, I was impressionable and thus, I became to believe the stereotypes that white people had money and were not dangerous and that First Nations people were poor and scary. Another common myth that I grew up believing was the idea that all people have equal opportunities and that people who are poor simply don’t try. Lastly, I engaged with the girl/boy gender binary and developed understandings of internalized gender roles. Being a twin, I thought it was adorable when my twin and I had matching outfits in contrasting colours and thus, I failed to understand the problematic nature of becoming absorbed by the socially developed gender categories. Due to my experiences as a child, I have blurred lenses concerning gender, classism, racism and being Canadian that guide the way I “read the world”.

My experiences above illustrate examples of single stories that I was taught throughout my schooling and demonstrates how the lens of white, European, wealthy, males was the truth that mattered. I developed an ignorance towards Canada’s true history and believed the myths about classism because that’s what was being taught and never did I receive opportunities to consider these topics from the perspective of Indigenous people or individuals living in poverty. Students are taught to believe the information shared by their teachers and thus, it is my role as an educator to ensure that I teach from various perspectives and provide my students with opportunities to consider material from points of view differing from their own. I hope to teach my students to acknowledge that they have personal biases and instill in them a willingness to challenge oppressive perspectives.

Through my journey in the faculty of education thus far, I have learned about the importance of unlearning the biases we develop from our personal experiences. I believe that the best way to do this is to first acknowledge that I do have biases and then reflect on why they exist. I cannot change my personal experiences growing up but I can move forward in allowing myself to feel uncomfortable and discussing the socially constructed ideas, normative narratives, binaries, oppression, discrimination, and rebuttals created by the identities that I have come to understand through my upbringing. I am a white, middle-class, Canadian female and by appropriately owning these identities and acknowledging the privileges and oppression that each of those identity features offers me I will begin to unlearn the biases that I have developed in regards to them. Beyond owning up to my personal lenses that I use to view the world, I must also be open to learning about perspectives that differ from my own views as I strive to work towards a more accepting and diverse lens that accounts for a variety of perspectives. As a pre-service educator, I am committed to being a life-long learner who is willing to feel uncomfortable and ask myself the tough questions when I notice myself having bias thoughts.

 

 

We are all Mathematical Beings

This week’s focus on curriculum as numeracy sparked my attention and challenged me to question how the way math is being taught in schools is oppressive and strictly addresses the dominant worldview. Eddie Woo’s Ted Talk, the assigned chapter from Jagged Worldviews CollidingTeaching Mathematics and the Inuit Community and Dr. Gale Russell‘s engaging presentation all provided me with various perspectives concerning teaching and learning mathematics.

Reflecting on my experiences in mathematics illustrates how the way mathematics is taught in schools does not create equitable learning opportunities for all students. The concept of accepting and embracing all ways of thinking and knowing is not new to me as it was consistently stated in my classrooms that everyone thinks differently, however, beyond stating this comment, the belief was rarely implemented in classrooms and often entirely contradicted. In my math classrooms the phrase “math is universal” was often expressed and personally, this became something I adored about the subject because I viewed it as a language for global communication. Reflecting on my experiences illustrates how the belief that math is universal is a myth, and in reality, the way mathematics is being taught is extremely culturally biased. For example, I learned math through the base-10 numerical system and it was critical that I understood the word equal to mean “the exact same” in order to be successful in my math classes. What about students who grew up being exposed to different numerical systems or have been taught alternative meanings for the word equal? How is this fair to them?  I was also trained to reiterate formulas, practice repetition, and memorize multiplication tables to ensure I would perform well on tests. Personally, I was successful in this system and the affirmation I received from my test marks motivated my positive attitude towards math. Due to my personal passion for mathematics, I also challenged myself to learn the “why” concerning what I was being taught so that I could justify my work.  But what about students who struggle with writing exams and did not put in the effort to learn what isn’t being explicitly taught? Is this system doing them an injustice? I believe that even students who prosper in math classrooms may be missing out on the possibility of developing deep understandings due to the emphasis placed on simply doing well on exams. Another problematic result of the way math is being taught is that many students develop negative attitudes towards math and the belief that they simply “do not get math” early on in their schooling. This attitude follows them and may cause them to choose to take the pathways of math stereotyped to be easier or totally avoid taking math classes which may hinder their opportunities in the future. Math is everywhere in our world, utilized by everyone, and rooted deeply in daily activities. Unfortunately, the way math is being taught in schools makes the subject appear daunting for some students, separate from everyday life and does not permit one’s culture and community to have a role in the learning process.

Eurocentric views of mathematics control the school system but despite their dominance, other brilliant perspectives of mathematics do exist and are deserving of being acknowledged and implemented. Louise Poirier discusses Inuit Mathematics which is very different from the math that I have been taught proving that the belief that “math is universal” is a myth and that what I believe to be common sense in math is not the same for everyone. For the Inuit culture, mathematics is performed under the base 20 numerical system which is vastly different from performing mathematical operations in the base 10 system that dominates the school system. Their reason for using base 20 follows that humans have 20 digits (fingers and toes combined) which I believe is both brilliant and logical. The second big difference I noticed between Inuit mathematics and Eurocentric mathematics is the gap that occurs when translating words between the two languages. For example, “line” in Eurocentric mathematics is automatically assumed to be straight but in Inuit mathematics, the term “line” does not imply straight. This is due to the reason that straight lines are far to come by in nature and the Inuit people place a great emphasis on learning from the land. This also connects to how in Inuit mathematics they do not have measuring tools such as rulers or compasses but rather they use objects found in nature or their limbs for the purpose of measuring. What was most interesting for me is that in Inuit mathematics, they do not have symbols for representing numbers because they simply represent numbers orally and a number without context has no meaning in their culture. Thus, they do not use formulas or perform hand-written operations which are highly emphasized in Eurocentric mathematics.

Exploring Inuit mathematics, taught me that my way of understanding mathematics is not the only way and that as an educator, I will need to be cautious when teaching math and ensure that I am not blinded by the commonsense understandings of mathematics that I have become engrained with throughout my schooling. We are ALL mathematical beings, and it is my goal to develop a classroom where ALL students are inspired to discover their mathematical abilities and learn math from various perspectives.

 

Curriculum as Citizenship

As the semester progresses, I am continually being exposed to ideas of curriculum that do not fit the common-sense understanding instilled in society regarding curriculum. Beyond formal curriculum which outlines outcomes and indicators for specific subject areas, curriculum as citizenship is also important to consider as educators. I believe that all educators would agree that we are accountable for guiding our students to become “good” citizens but the question then becomes, what makes a citizen “good”? Joel Westheimer outlines three kinds of citizens in his paper concerning the politics of educating for democracy and although they could all be classified as “good”, there are obvious variances between the three types. Firstly, the personally responsible citizen is law-abiding, recycles, pays taxes, and contributes to community fundraisers and collections. If we consider a food drive as an analogy, the personally responsible citizen is an individual who donates cans and other items. Secondly, the participatory citizen actively engages in activities concerning civic affairs and the social life of their community. Rather than simply donating cans, participatory citizens plan, organize, and advertise food drives in their communities. Lastly, the justice-oriented citizen focuses on addressing the root causes of social issues and actively strives for solutions. In our analogy, justice-oriented citizens are individuals who ask the question “why are people hungry?” and work towards finding solutions for their discoveries. The three kinds of citizens all place emphasis on different aspects of being a community member and express distinct societal values. Thus, as educators, we must be cautious about where we place emphasis concerning appropriate citizen behaviour and ensure that a balance of the three kinds of citizens is being encouraged in our classrooms.

Despite not always being specifically defined, my experiences as a student taught me many things concerning how to be a “good” citizen. Emphasis on being a personally responsible citizen could be seen through simple lessons such as sharing, recycling, collecting food, mitts and toques, or Christmas hamper items, and abiding by the rules of the school. I was also expected to obtain volunteer hours in my high school Christian Ethics courses. By encouraging volunteering, donating, tidiness, and following rules, my schools taught me that “good” citizens must partake in activities of similar nature. Unfortunately, hidden behind these positive concepts is the idea that if you are less fortunate and unable to help the poor than you are not a “good” citizen which marginalizes oppressed groups of the population. Students were also awarded for their personal responsible actions which may have been the reason for their behaviours rather than investing their time simply because they believed it was the right thing to do. Through student-led programs such as SLC (Student Leadership Council), Peacekeepers, and safety patrollers, my schools illustrated the importance of being a participatory citizen. They exemplified how not only is it important for citizens to do their individual part but that “good” citizens also contribute to planning and organizing events or activities that impact their communities as a whole. The concept of the justice-oriented citizen was probably the least promoted but can still be seen when reflecting on aspects of the hidden curriculum. Many essay topics or questions on exams and assignments permitted me to critically think about the topics under study and share my personal opinions which provided me with a voice and did not encourage compliance. Teaching students to critically think helps inspire them to ask difficult questions and challenge the norms which are qualities of justice-oriented citizens.

Embedded in the curriculum are lessons about being a citizen. It is important to remember that despite all three kinds of citizens described by Joel Westheimer being “good”, they must all be emphasized appropriately.  Schools tend to overemphasize the need for students to be personally responsible by celebrating individual behaviours and encouraging students to feel good about their personal contributions. To truly be “good” citizens, I believe students must learn to challenge social normatives in hopes of improving societal norms for all citizens and to act selflessly without the desire for acknowledgment. As an educator, I am accountable for teaching my students about citizenship and thus it will be my duty to set a positive example of what being a “good” citizen looks like.

We are Responsible for Treaty-Education

As part of my classes for my three-week block, I have picked up a Social Studies 30 course. This past week we have been discussing the concept of standard of living and looking at the different standards across Canada. I tried to introduce this concept from the perspective of the First Nations people of Canada and my class was very confused about the topic and in many cases made some racist remarks. I have tried to reintroduce the concept but they continue to treat it as a joke.

The teachers at this school are very lax on the topic of Treaty Education as well as First Nations ways of knowing. I have asked my Coop for advice on Treaty Education and she told me that she does not see the purpose of teaching it at this school because there are no First Nations students. I was wondering if you would have any ideas of how to approach this topic with my class or if you would have any resources to recommend.

 -anonymous student

To anonymous student,

Thank you for reaching out to me. Treaty Education is not only mandatory in the Saskatchewan curriculum and thus, our responsibility to teach, but also a very important subject to address in order to move away from teaching colonialism and racism in the underlying curriculum and stride towards instilling true understandings about the history of our country among our students. Unfortunately, treaty-education makes many educators feel uncomfortable and challenges them to unlearn the societal narratives that they were raised with and change their perspectives concerning what it truly means to be a treaty person. Many of your students may have reacted the way they did due to a lack of understanding or misinformation about First Nations people in Canada which reiterates the importance of teaching Treaty-Education.

I believe that a strong starting point for teaching Treaty-Education is developing the understanding that we are all Treaty people. Personally, this idea was only introduced to me in my first year of University and initially, it was unsettling to hear because my mindset was that I was not a First Nations, Metis, or Inuit person and thus, I was not a treaty person. Today, I recognize the harm in that belief and can now comfortably acknowledge that I am a treaty person because treaties were agreed upon between Indigenous people and European people from whom I descend on the covenant “as long as the sun shines and the rivers flow” which implies that they will always exist. In fact, living in Canada, we are all treaty people. As Canadians, we all inherit the outcomes of treaties and experience the effects of them every day. The decisions of the past have created the future of today and we must acknowledge them and learn the truth about our countries past which begins long before European settlement.  Reading Cynthia Chamber’s chapter and sharing it with your coop teacher and students may help instill this perspective and make them more open to learning about treaties and their continuous effects on our country.

With the understanding that we are all treaty people, it should become evident why no matter what race we belong to, Treaty-education is part of every Canadian’s identity and should be taught to all students. Many Indigenous students have knowledge about Treaty-education and indigenous people’s history of our land and as Claire suggests in her introduction video, Indigenous peoples of Canada “do not want more cultural programming … especially when these programs are aimed at them specifically.” What Indigenous students want is to be treated fairly, for the colour of their skin not be a barrier to their success, and for their classmates to know and understand the things that they know and understand about being indigenous. Treaty-education goes far beyond teaching about our countries past because it demonstrates respect and admiration for the people who began on our land and have experienced detrimental effects due to white European settlement. For these reasons, Treaty-education must be taught to ALL students.

Our society has become instilled with racism which is “pervasive, insidious, and deadly” as expressed by Claire in her introduction. News stories such as the Colten Boushie case exemplify this idea and can be used in our classrooms to illustrate the truth about racism in our province. Recent examples concerning the effects of treaties that are still relevant today should help students understand the seriousness of Treaty-education and be open to the learning process. I recommend including such stories in your lessons to help the concept of Treaty-eduction to become real and present in the eyes and minds of your students rather than simply a topic of our past.

My final advice to you is to keep talking. The more we discuss Treaty-education, the more natural it will become and the more willing people will be to continue the conversations. Residential schools may no longer exist but their mentality remains constant and in order to fix that, we need to be honest about our countries past and embed our curriculum with Treaty-education rather than colonialism and racism which continue to persist. By taking responsibility for Treaty-education, we are putting ourselves in a position that will permit reconciliation and a more optimal future where everyone matters and has a voice to be heard.

Wishing you all the best,

Kendall Schneider

Learning From Place

Learning from Place: A Return to Traditional Mushkegowuk Ways of Knowing is an article that discusses the nature and power of learning from place. The article illustrates the reflection of a research project that was conducted to honor the Mushkegowuk Cree people’s concepts of land, environment, and nature. By sharing the story of the river excursion which joined many generations from youth to elders, the importance of learning from experience and storytelling were conveyed which are two key ideas of the indigenous ways of knowing.

The article explains how decolonization cannot be limited to rejecting and transforming normative narratives but rather must also depend on recovering and renewing mentorship and intergenerational relationships. Thus, the river excursion which allowed individuals from vast generations to travel together and communicate with one another demonstrates many forms of decolonization and reinhabitation. While on the voyage, youth, adults, and elders learned about the history and significance of the river, related issues of governance and land management, and the culture of the community. A key theme was the importance of nature and land for the Muskegowick people which is more than just a resource; it is a spiritual and material place that all life springs from and the cultural identity of the people. The word The large focus on the word ‘paquataskamik’ which means “natural environment” was emphasized in explaining the traditional views of the land. The elders were also able to share many vibrant meanings of the river that go well beyond thinking of it as simply a body of water. The Mushkegowuk people saw the river as a way of life and believe that it has physical, spiritual, and emotional uses and meanings. The river is also used as a cemetery and it is expected that when traveling along the river those who have passed away remain in ones’ thoughts and prayers. The group also documented sites of significance for the community during the excursion which encourages reinhabitation of the land. Most importantly, while on the trip, an audio documentary was recorded to detail the experience of the travelers. Many voices such as those from members of the band office, health center,  and education system, were included allowing for community involvement beyond those participating in the excursion. The documentary was shared with the community and broadcasted on the radio in hopes of reaching a broad audience and allowing their stories and traditional knowledge to be heard and preserved for future generations to come. Reinhabitation and decolonization are dependent on one another but both rely on identifying a need for change regarding the use of land and ways of thinking and the river excursion, which helped members of the community share linguistic, cultural, historical, and geographical knowledge permitted for these realizations to occur.

After reading the article, I realize the significance of teaching from place and being aware of the traditional understandings of the community that I will be teaching in. Acknowledging my position in a given community will require me to commit to unlearning and relearning new perspectives and provide me with insight into the perceptions my students hold. It is important that I recognize my personal biases and remain aware of my own beliefs while being open to change and accepting of new ideas. I must remember that knowledge and curriculum can come from more than just textbooks and government regulated materials and that it is okay to ask for help when I do not feel confident in my knowledge about particular subject areas. Bringing elders and other voices into my classrooms will allow my students to learn from experts in their fields who can speak from experience and provide my students with true understandings. Encouraging learning from place in my classroom will require me to first acknowledge my position in the community but more importantly incorporate significant local knowledge and values into everyday classroom lessons.

 

 

The Truth About Curriculum

Before Reading: 

I honestly never questioned the ‘how’ of curricula creation, but putting that into words makes me think that as a preservice educator, I definitely should. My understanding of how school curricula are developed stems from my personal experience in the Saskatchewan school system and the little discussion through some of my education courses thus far. I think curricula are developed by a group of people with some expertise or relation to the field of education whether that being that they had teaching experience or not. They decide what is critical for students to learn at each particular grade level and organize these ideas into outcomes and indicators in hopes that all educators are able to successfully cover the outlined topics in a given school year. When deciding what is important, I believe that society has a heavy influence and thus white eurocentric views continue to guide the decisions. I also know that in Canada, school curricula are provincially mandated thus I think provincial governments have the final say in what is implemented across the province. Once curriculum guidelines have been agreed upon, they become the new norm and are executed across the province. 

After Reading:

After reading Ben Levin’s chapter regarding curriculum policy and politics concerning what should be learned in schools I realized my understanding of curriculum development was fairly minimal and vague. Today, curricula are developed by bringing groups of experts together to draft new or revised versions by examining and evaluating current forms of curricula and suggestions for change that have been made. The two big concerns when designing curriculum are ‘what subjects should be taught ‘ and ‘what content should be included under each subject’ and there are various opinions regarding these questions. Curriculum decisions are shaped largely by “ideology, personal values, issues in the public domain, and individual interests” and because everyone has some relation to schooling, their personal experiences in school have a grand influence on educational policies. Post-secondary schools also have a significant influence due to the entrance requirements they have for students interested in enrolling in their programs. Levin opened my eyes to the power of politics regarding curriculum design and thus the influence that the economy and people in authoritative positions have on deciding what should be taught in schools. Levin also pointed out that once a curriculum has been approved by the provincial government, it is not always implemented successfully in schools because teachers’ practices are often influenced by what they know and value, and what is practical for them to implement.

I have learned that I was correct in thinking that the provincial government has the final authority when developing school curricula. Thus, “an individual in a key position can either shape of hold up decisions” despite the opinions of others which is concerning as one person in power should not have the authority to influence the lives of all students and the future generations of our society. The significant influence of one individual shifts the focus from being on providing sufficient education for all students, to meeting biased goals. Often experts in a particular subject area are consulted when making the decisions about what should be included but this can also be problematic because the result of expert dominated choices will only be implemented successfully by other masters of the subject. The reality is that most teachers, especially those with elementary education degrees, will have limited knowledge in particular subject areas and will not be able to teach the objectives developed by experts. I believe what is most problematic is that despite new curricula being developed, they are not being implemented appropriately in classrooms. For example, treaty education was introduced to Saskatchewan’s curriculum in 2007 and yet students are still not learning the truth about treaties in their classrooms. Designing curricula is a political process which means it is driven by the most vocal interests and marginalizes opinions of those whose matter. Levin’s chapter exposed me to the troubling truths about the process of designing curricula and emphasized the importance of considering who is designing curricula.

Troubling Aspects of the “Good” Student

Common-sense ideas have been developed by the dominant culture of society and instilled in us through the varying social influences that we are surrounded by. The narratives tell us how individuals should behave in particular situations and provide guidelines that everyone should abide by despite never being explicitly taught to do so. According to the common-sense structured in our society, there is one and only one definition of a “good” student. “Good” students are compliant, obedient and focused. They sit quietly in their desks, raise their hands to ask permission to speak, and do not question the material being taught. In Kumashiro’s chapter, he states that due to common-sense he has been exposed to, he once believed “learning meant completing certain assignments and repeating on exams the correct definitions or themes” leaving no room for the expression of personal reflections or perspectives. Common sense tells us that “good” students are always present, and diligently meet all the requirements of their assignments on time permitting them to consistently receive high grades. Unfortunately, these common-sense ideas are oppressive and do not encourage students to critically think.

The common-sense definition of the “good” student privileges pupils who belong to the dominant culture and are fully aware of what is expected of them in this context. Those who have grown up with the common-sense beliefs are not challenged to unlearn their ideas of what makes a “good” student and relearn new notions, and thus they are naturally able to adapt to the normative trends.  Students who have a particular learning style that permits them to memorize information and regurgitate it on standardized exams also benefit from the common-sense description. If one requires hands-on work, time to reflect and question the lectured information, and activity breaks to avoid becoming restless, they will be disadvantaged and their performance will not live up to the expectation of a “good” student. Learning for students who were influenced by common-sense values that vary from those of the authoritative culture will also be hindered. By allowing common-sense to control the thoughts around what makes a “good” student, only those who belong to the dominant clique and fit the normative learning style have the opportunity to be considered successful.

The concept of a “good” student eliminates the possibility to see changes in our society towards social justice. The common-sense definition of a “good” student is strictly one perspective and despite having some strengths, the weaknesses are apparent as it insists on compliance and privileges students who fit the norm. By valuing obedience in our school systems, we are teaching students to be compliant citizens rather than encouraging them to wonder, question, and challenge the social norms. Obedience also eliminates the opportunity for collaborative reflection which would permit varying perspectives to be shared and create opportunities for students to learn from their peers. Adopting the common-sense idea regarding “good” students permits students to resist learning things that reveal the problematic nature of an individual’s partial knowledge which allows the troubling normative stories to continue to shine and disregards the need for change. Every individual has some knowledge, but if we are resistant to questioning our personal beliefs, the dominant culture in society will continue to control our ways of thinking.

The Significance of Reflection

“We do not learn from experience… we learn from reflecting on experience.”

– John Dewey

            John Dewey was a progressive educational theorist who stressed the idea that education is a valuable experience rather than simply preparation for future life experiences. He believed in active learning and recognized the advantages of being able to personally experience learning. His quote, “We do not learn from experience… we learn from reflecting on experience” caught my attention as I believe it is important for educators to understand. Due to taxing curriculum guidelines and time restraints of course semesters, educators often teach their students instrumentally in order to meet all of the required objectives. In a jarring articleRichard Skemp describes instrumental understanding as strictly offering concrete instructions on how to solve problems given specific starting and end points but not providing any justification for the directions. Thus, students memorize steps for the sole purpose of the end result and do not develop a complete understanding of the topic that they can carry with them and apply to other problems. In contrast, relational understanding provides students with a diverse knowledge base pertaining to a subject area that is independent of the end results of particular questions by including valid explanations as to how and why the process being taught works. As Mason states in Thinking Mathematically, “without reflection, practice can wash over you, leaving no permanent marks” (2010, p.136). Dewey’s words remind educators of the importance of teaching their students relationally,  reflecting on experiences and critically analyzing material in order to gain advantageous understandings.

The reflection phase of learning can include many different strategies such as checking for mistakes, asking questions to gather information as to why the steps that were taken were valid, attempting to represent the solution in a different form, considering alternative methods to finding the solution, making connections, or extending the problem further. During the reflection process, students become fully engaged with the material and build an understanding of what is actually being taught rather than simply trusting the educator and memorizing the process. It is human nature to be curious, ask questions, and notice discrepancies and students deserve the opportunity to act on their eager attitudes towards learning. As Dewey suggests, it is only when students are provided with time to reflect on their experiences that they truly begin to learn. I believe that contradicting opinions, alternative methods of solving problems and interactive class discussions can become educational figures that students can learn from rather than strictly relying on the perspectives that their teachers offer.

As a future educator, I recognize that providing students with sufficient time to reflect on their work may not always be easy similarily to how it was when I was a student. Educators are under extreme pressure to meet curriculum guidelines and time to stray away from course objectives and explore reflective thoughts may not always be available. Permitting time for reflection will require educators to be open to questions or comments that will cause tangents in their lesson plans and intrude on scheduled learning. Allowing reflection will also mean that students’ learning will be guided by their own voices and the discussion that results due to the contributions from many members of the classroom. This could result in students learning variations of material making it impossible for students in different classrooms to have the same learning experiences. The question then becomes, is it more important for every student to learn the same thing or for students’ probabilities of learning to be as high as they can be? During these situations, it will be important to remember that although educators are hired to teach the curriculum, they are responsible for their students’ learning and by promoting reflection, we are able to provide our students with the best atmosphere to expand their knowledge.

Mason, J., Burton, L., & Stacey, K. (2010) Thinking Mathematically. Harlow, England: Pearson Education Limited.